Finite Group Databasebeta

← C43×#18597 #24938614

Subgroups — C43×#18597 #24938614

Order 11008.

876 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3515C211yesmaximal, characteristic
2C43×#3252C211yesmaximal, characteristic, complemented
3C43×#3185C211yesmaximal, characteristic, complemented
4C43×#3076C211yesmaximal, characteristic, complemented
5C43×#1654C211yesmaximal, characteristic, complemented
6C43×#1653C211yesmaximal, characteristic, complemented
7C43×#1644C211yesmaximal, characteristic, complemented
8C43×#1643C211yesmaximal, characteristic, complemented
9C43×#1636C211yesmaximal, characteristic, complemented
10C43×#1635C211yesmaximal, characteristic, complemented
11C43×#1632C211yesmaximal, characteristic, complemented
12C43×#1632C211yesmaximal, characteristic, complemented
13C43×#1550C211yesmaximal, characteristic, complemented
14C43×#1489C211yesmaximal, characteristic, complemented
15C43×#1483C211yesmaximal, characteristic, complemented
16C43×#557C2211yescharacteristic
17C43×#554C2211yescharacteristic
18C43×#554C2211yescharacteristic
19C43×#553—21no—
20C43×#552—21no—
21C43×#552—22no—
22C43×#552—21no—
23C43×#547—21no—
24C43×#547C2211yescharacteristic
25C43×#541—21no—
26C43×#539—22no—
27C43×#533C2211yescharacteristic
28C43×#533C2211yescharacteristic
29C43×#529—21no—
30C43×#529C2211yescharacteristic
31C2×#125×C43—21no—
32C43×#520—21no—
33C4×#41×C43C2211yescharacteristic
34C43×#498C2211yescharacteristic
35C43×#494C2211yescharacteristic
36C43×#487C2211yescharacteristic
37C43×#487C2211yescharacteristic
38C43×#479—21no—
39C43×#479—21no—
40C43×#478—21no—
41C43×#477C2211yescharacteristic
42C43×#477C2211yescharacteristic
43C43×#476C2211yescharacteristic
44C43×#476C2211yescharacteristic
45C43×#475C2211yescharacteristic
46C43×#474C2211yescharacteristic
47C43×#470—22no—
48C43×#470—21no—
49C43×#468—21no—
50C43×#464—21no—
51C43×#462C2211yescharacteristic
52C43×#461C2211yescharacteristic
53C43×#441—22no—
54C43×#427—21no—
55C43×#423C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C43×#416—21no—
58C4×M16×C43C2211yescharacteristic
59C43×#333C2211yescharacteristic
60C43×#333C2211yescharacteristic
61C43×#332C2211yescharacteristic
62C43×#332C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×Q8⋊C8C2211yescharacteristic
67C43×D4⋊C8C2211yescharacteristic
68C43×D4⋊C8C2211yescharacteristic
69C43×D4⋊C8C2211yescharacteristic
70C43×D4⋊C8C2211yescharacteristic
71C2×#41×C43—21no—
72C2×#41×C43D411yescharacteristic
73C2×Q16×C43—22no—
74C2×Q16×C43—21no—
75C2×SD16×C43—21no—
76C2×M16×C43—21no—
77C2×M16×C43—21no—
78C22×C8×C43—21no—
79C4⋊Q8×C43—21no—
80C4⋊Q8×C43C2311yescharacteristic
81C4⋊Q8×C43C2311yescharacteristic
82C4⋊Q8×C43C2311yescharacteristic
83C4⋊Q8×C43C2311yescharacteristic
84#126×C43—22no—
85#126×C43—22no—
86#126×C43—22no—
87#126×C43—21no—
88#125×C43—22no—
89#125×C43—22no—
90#125×C43—22no—
91#125×C43—21no—
92#125×C43—21no—
93#125×C43—22no—
94#125×C43—21no—
95#125×C43—21no—
96#125×C43—21no—
97#125×C43D411yescharacteristic
98#124×C43D411yescharacteristic
99#123×C43—22no—
100#123×C43—22no—
101#123×C43—22no—
102#123×C43—21no—
103#123×C43—22no—
104C22⋊Q8×C43—21no—
105C22⋊Q8×C43—22no—
106C22⋊Q8×C43—22no—
107C22⋊Q8×C43—21no—
108C22⋊Q8×C43—21no—
109C22⋊Q8×C43—21no—
110C22⋊Q8×C43—21no—
111C22⋊Q8×C43—21no—
112C22⋊Q8×C43D411yescharacteristic
113C22⋊Q8×C43D412yes—
114#121×C43—22no—
115#121×C43—21no—
116#121×C43D411yescharacteristic
117C4×Q8×C43—21no—
118C4×Q8×C43—21no—
119C4×Q8×C43—21no—
120C4×Q8×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43D412yes—
124C4×Q8×C43C2311yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43D411yescharacteristic
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#117×C43—22no—
137#117×C43—22no—
138#117×C43—21no—
139#117×C43—21no—
140#117×C43—21no—
141#117×C43—21no—
142#117×C43D411yescharacteristic
143C2×C4⋊C4×C43—22no—
144C2×C4⋊C4×C43—22no—
145C2×C4⋊C4×C43—21no—
146C2×C4⋊C4×C43—21no—
147C2×C4⋊C4×C43—21no—
148C2×C42×C43—21no—
149C2×C42×C43C2311yescharacteristic
150#107×C43—21no—
151#107×C43—21no—
152#107×C43—21no—
153#106×C43—22no—
154#106×C43—21no—
155#106×C43—21no—
156#106×C43—21no—
157C4⋊C8×C43—21no—
158C4⋊C8×C43—21no—
159C4⋊C8×C43C2311yescharacteristic
160C4⋊C8×C43C2311yescharacteristic
161C4⋊C8×C43C2311yescharacteristic
162C4⋊C8×C43C2311yescharacteristic
163#103×C43—21no—
164#103×C43—21no—
165#103×C43—22no—
166#103×C43—21no—
167#103×C43—22no—
168#103×C43—21no—
169#103×C43—21no—
170#102×C43—21no—
171#102×C43—21no—
172#102×C43—21no—
173#97×C43—21no—
174C4×C8×C43C2311yescharacteristic
175C4×C8×C43C2311yescharacteristic
176#41×C43—22no—
177#41×C43—41no—
178#41×C43—42no—
179#41×C43—42no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43C2×D411yescharacteristic
184C2×Q8×C43C2×D411yescharacteristic
185C2×Q8×C43C2×D412yes—
186C2×D4×C43—22no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43C2×D411yescharacteristic
190C2×D4×C43C2×D411yescharacteristic
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201Q16×C43—44no—
202Q16×C43—81no—
203SD16×C43—81no—
204M16×C43—42no—
205M16×C43—81no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—42no—
213C4⋊C4×C43—22no—
214C4⋊C4×C43—22no—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—22no—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43—22no—
220C4⋊C4×C43—22no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—22no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—41no—
237C4⋊C4×C43—41no—
238C4⋊C4×C43C2×D411yescharacteristic
239C4⋊C4×C43C2×D412yes—
240C4⋊C4×C43C2×D411yescharacteristic
241C4⋊C4×C43C2×D411yescharacteristic
242C4⋊C4×C43C2×D411yescharacteristic
243C22⋊C4×C43—22no—
244C22⋊C4×C43—22no—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—21no—
248C22⋊C4×C43—21no—
249C22⋊C4×C43—21no—
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—21no—
254C22⋊C4×C43—21no—
255C22⋊C4×C43—41no—
256C42×C43—22no—
257C42×C43—21no—
258C42×C43—21no—
259C42×C43—22no—
260C42×C43—21no—
261C42×C43—21no—
262C42×C43—41no—
263C42×C43C2×D411yescharacteristic
264C42×C43C2×D411yescharacteristic
265C42×C43C2×D411yescharacteristic
266C42×C43C2411yescharacteristic
267C23×C43—21no—
268C23×C43—21no—
269C23×C43#12011yescharacteristic
270Q8×C43—21no—
271Q8×C43—21no—
272Q8×C43—21no—
273Q8×C43—21no—
274Q8×C43—42no—
275Q8×C43—42no—
276Q8×C43—41no—
277Q8×C43—41no—
278Q8×C43—41no—
279Q8×C43—41no—
280D4×C43—21no—
281D4×C43—21no—
282D4×C43—21no—
283D4×C43—42no—
284D4×C43—44no—
285D4×C43—81no—
286D4×C43#13712yes—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—41no—
300C2×C4×C43—42no—
301C2×C4×C43—44no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—81no—
309C2×C4×C43—82no—
310C2×C4×C43—82no—
311C2×C4×C43#12011yescharacteristic
312C2×C4×C43#12011yescharacteristic
313C2×C4×C43#12011yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C22×D411yescharacteristic
317C8×C43—22no—
318C8×C43—41no—
319C8×C43—41no—
320C8×C43—41no—
321C8×C43—41no—
322C8×C43—41no—
323#18597C4311yesmaximal, characteristic, direct product factor, Sylow
324C22×C43—22no—
325C22×C43—21no—
326C22×C43—21no—
327C22×C43—21no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43C2×#12011yescharacteristic
334C4×C43—21no—
335C4×C43—21no—
336C4×C43—21no—
337C4×C43—21no—
338C4×C43—41no—
339C4×C43—41no—
340C4×C43—42no—
341C4×C43—41no—
342C4×C43—41no—
343C4×C43—41no—
344C4×C43—41no—
345C4×C43—42no—
346C4×C43—81no—
347C4×C43—81no—
348C4×C43C2×#13711yescharacteristic
349C4×C43#57511yescharacteristic
350C4×C43#57711yescharacteristic
351C4×C43#57811yescharacteristic
352#3515C2×C4311yescharacteristic
353#3252C2×C4311yescharacteristic, complemented
354#3185C2×C4311yescharacteristic, complemented
355#3076C2×C4311yescharacteristic, complemented
356#1654C2×C4311yescharacteristic, complemented
357#1653C2×C4311yescharacteristic, complemented
358#1644C2×C4311yescharacteristic, complemented
359#1643C2×C4311yescharacteristic, complemented
360#1636C2×C4311yescharacteristic, complemented
361#1635C2×C4311yescharacteristic, complemented
362#1632C2×C4311yescharacteristic, complemented
363#1632C2×C4311yescharacteristic, complemented
364#1550C2×C4311yescharacteristic, complemented
365#1489C2×C4311yescharacteristic, complemented
366#1483C2×C4311yescharacteristic, complemented
367C2×C43—41no—
368C2×C43—42no—
369C2×C43—81no—
370C2×C43#300711yescharacteristic
371C2×C43#301311yescharacteristic
372C2×C43#301811yescharacteristic
373#557C22×C4311yescharacteristic
374#554C22×C4311yescharacteristic
375#554C22×C4311yescharacteristic
376#553—21no—
377#552—21no—
378#552—22no—
379#552—21no—
380#547—21no—
381#547C22×C4311yescharacteristic
382#541—21no—
383#539—22no—
384#533C22×C4311yescharacteristic
385#533C22×C4311yescharacteristic
386#529—21no—
387#529C22×C4311yescharacteristic
388C2×#125—21no—
389#520—21no—
390C4×#41C22×C4311yescharacteristic
391#498C22×C4311yescharacteristic
392#494C22×C4311yescharacteristic
393#487C22×C4311yescharacteristic
394#487C22×C4311yescharacteristic
395#479—21no—
396#479—21no—
397#478—21no—
398#477C22×C4311yescharacteristic
399#477C22×C4311yescharacteristic
400#476C22×C4311yescharacteristic
401#476C22×C4311yescharacteristic
402#475C22×C4311yescharacteristic
403#474C22×C4311yescharacteristic
404#470—22no—
405#470—21no—
406#468—21no—
407#464—21no—
408#462C22×C4311yescharacteristic
409#461C22×C4311yescharacteristic
410#441—22no—
411#427—21no—
412#423C22×C4311yescharacteristic
413C2×C4⋊C8C22×C4311yescharacteristic
414#416—21no—
415C4×M16C22×C4311yescharacteristic
416#333C22×C4311yescharacteristic
417#333C22×C4311yescharacteristic
418#332C22×C4311yescharacteristic
419#332C22×C4311yescharacteristic
420Q8⋊C8C22×C4311yescharacteristic
421Q8⋊C8C22×C4311yescharacteristic
422Q8⋊C8C22×C4311yescharacteristic
423Q8⋊C8C22×C4311yescharacteristic
424D4⋊C8C22×C4311yescharacteristic
425D4⋊C8C22×C4311yescharacteristic
426D4⋊C8C22×C4311yescharacteristic
427D4⋊C8C22×C4311yescharacteristic
428C43#1859711yescharacteristic, direct product factor, Sylow
429C2×#41—21no—
430C2×#41D4×C4311yescharacteristic
431C2×Q16—22no—
432C2×Q16—21no—
433C2×SD16—21no—
434C2×M16—21no—
435C2×M16—21no—
436C22×C8—21no—
437C4⋊Q8—21no—
438C4⋊Q8C23×C4311yescharacteristic
439C4⋊Q8C23×C4311yescharacteristic
440C4⋊Q8C23×C4311yescharacteristic
441C4⋊Q8C23×C4311yescharacteristic
442#126—22no—
443#126—22no—
444#126—22no—
445#126—21no—
446#125—22no—
447#125—22no—
448#125—22no—
449#125—21no—
450#125—21no—
451#125—22no—
452#125—21no—
453#125—21no—
454#125—21no—
455#125D4×C4311yescharacteristic
456#124D4×C4311yescharacteristic
457#123—22no—
458#123—22no—
459#123—22no—
460#123—21no—
461#123—22no—
462C22⋊Q8—21no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8D4×C4311yescharacteristic
471C22⋊Q8D4×C4312yes—
472#121—22no—
473#121—21no—
474#121D4×C4311yescharacteristic
475C4×Q8—21no—
476C4×Q8—21no—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8D4×C4311yescharacteristic
481C4×Q8D4×C4312yes—
482C4×Q8C23×C4311yescharacteristic
483C4×Q8C23×C4311yescharacteristic
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4D4×C4311yescharacteristic
492C4×D4C23×C4311yescharacteristic
493C4×D4C23×C4311yescharacteristic
494#117—22no—
495#117—22no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117—21no—
500#117D4×C4311yescharacteristic
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C42—21no—
507C2×C42C23×C4311yescharacteristic
508#107—21no—
509#107—21no—
510#107—21no—
511#106—21no—
512#106—21no—
513#106—22no—
514#106—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8C23×C4311yescharacteristic
518C4⋊C8C23×C4311yescharacteristic
519C4⋊C8C23×C4311yescharacteristic
520C4⋊C8C23×C4311yescharacteristic
521#103—21no—
522#103—21no—
523#103—22no—
524#103—21no—
525#103—22no—
526#103—21no—
527#103—21no—
528#102—21no—
529#102—21no—
530#102—21no—
531#97—21no—
532C4×C8C23×C4311yescharacteristic
533C4×C8C23×C4311yescharacteristic
534#41—22no—
535#41—41no—
536#41—42no—
537#41—42no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C2×D4×C4311yescharacteristic
542C2×Q8C2×D4×C4311yescharacteristic
543C2×Q8C2×D4×C4312yes—
544C2×D4—22no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4C2×D4×C4311yescharacteristic
548C2×D4C2×D4×C4311yescharacteristic
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4C2×D4×C4311yescharacteristic
557C22×C4C2×D4×C4311yescharacteristic
558C22×C4C2×D4×C4311yescharacteristic
559Q16—44no—
560Q16—81no—
561SD16—81no—
562M16—42no—
563M16—81no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—42no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—41no—
595C4⋊C4—41no—
596C4⋊C4C2×D4×C4311yescharacteristic
597C4⋊C4C2×D4×C4312yes—
598C4⋊C4C2×D4×C4311yescharacteristic
599C4⋊C4C2×D4×C4311yescharacteristic
600C4⋊C4C2×D4×C4311yescharacteristic
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—41no—
614C42—22no—
615C42—21no—
616C42—21no—
617C42—22no—
618C42—21no—
619C42—21no—
620C42—41no—
621C42C2×D4×C4311yescharacteristic
622C42C2×D4×C4311yescharacteristic
623C42C2×D4×C4311yescharacteristic
624C42C24×C4311yescharacteristic
625C23—21no—
626C23—21no—
627C23#120×C4311yescharacteristic
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—21no—
632Q8—42no—
633Q8—42no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638D4—21no—
639D4—21no—
640D4—21no—
641D4—42no—
642D4—44no—
643D4—81no—
644D4#137×C4312yes—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—44no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—81no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4#120×C4311yescharacteristic
670C2×C4#120×C4311yescharacteristic
671C2×C4#120×C4311yescharacteristic
672C2×C4C22×D4×C4311yescharacteristic
673C2×C4C22×D4×C4311yescharacteristic
674C2×C4C22×D4×C4311yescharacteristic
675C8—22no—
676C8—41no—
677C8—41no—
678C8—41no—
679C8—41no—
680C8—41no—
681C22—21no—
682C22—22no—
683C22—21no—
684C22—21no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22C2×#120×C4311yescharacteristic
691C4—21no—
692C4—21no—
693C4—21no—
694C4—21no—
695C4—41no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4C2×#137×C4311yescharacteristic
706C4C43×#57511yescharacteristic
707C4C43×#57711yescharacteristic
708C4C43×#57811yescharacteristic
709C2—41no—
710C2—42no—
711C2—81no—
712C2C43×#300711yescharacteristic
713C2C43×#301311yescharacteristic
714C2C43×#301811yescharacteristic
subgroupG/H
center, socleC22×C43C2×#120
commutator, Frattini, cosocleC42C24×C43
prime radicalC43×#3515C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C43 ◁ C2×C42×C43 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C43×#3252C2semidirect
3. C43×#3185C2semidirect
4. C43×#3076C2semidirect
5. C43×#1654C2semidirect
6. C43×#1653C2semidirect
7. C43×#1644C2semidirect
8. C43×#1643C2semidirect
9. C43×#1636C2semidirect
10. C43×#1635C2semidirect
11. C43×#1632C2semidirect
12. C43×#1632C2semidirect
13. C43×#1550C2semidirect
14. C43×#1489C2semidirect
15. C43×#1483C2semidirect
323. #18597C43direct (N × H)
353. #3252C2×C43semidirect
354. #3185C2×C43semidirect
355. #3076C2×C43semidirect
356. #1654C2×C43semidirect
357. #1653C2×C43semidirect
358. #1644C2×C43semidirect
359. #1643C2×C43semidirect
360. #1636C2×C43semidirect
361. #1635C2×C43semidirect
362. #1632C2×C43semidirect
363. #1632C2×C43semidirect
364. #1550C2×C43semidirect
365. #1489C2×C43semidirect
366. #1483C2×C43semidirect
428. C43#18597direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C43×#35152
C43×#32522
C43×#31852
C43×#30762
C43×#16542
C43×#16532
C43×#16442
C43×#16432
C43×#16362
C43×#16352
C43×#16322
C43×#15502
C43×#14892
C43×#14832
#1859743